I would say don't bother stopping at Crewe (Heritage Centre a long way from the station, not particularly impressive last time I was there) but get off and walk round the walls at Chester. Make sure you have a [1/4"] map with you, sit on the RHS going on from Chester and enjoy the estuary/coastal views from there on.
It's a stiff walk from the station to the old city within the walls at Chester.
Best take a bus or taxi I would say, to Foregate St or Castle St, which are close to the centre.
Sundays on Avanti aren't always the best ride, and through trains to Chester/North Wales are the first to go if there is any disruption - you then have to rely on Transport for Wales.
The route is nice and rural for the most part after Watford, and once you hit the Dee estuary after Chester there are good views, particularly seawards.
There are old Soviet MiGs next to the line on the left at Broughton (Airbus factory).
The only through train I can see in May to fit your bill is the 1300 Euston-Holyhead (before the timetable change on the 18th).
Earlier than that you need to catch an Avanti train to Crewe and change to TfW.
On May 18 I can see replacement buses are involved Rhyl-Llandudno Jn, so that's a date to avoid.
On May 25 the replacement buses run from Chester to Llandudno Jn.
Travel on May 4 from Euston looks horrific (this is a bank holiday weekend with major engineering work).
The railway, particularly the WCML is not at its best on Sundays.
I doubt you'll have time for local excursions if you must be in Llandudno by 1800.
Try fastjp for options.
www.fastjp.com
